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Quantum Mechanics of Nanoparticles

Quantum Light Shaping for Measurement and Control

The precise measurement and control of complex systems, such as semiconductors and other solids, require the ability on the part of researchers to determine the distribution of photons in laser light among possible quantum states. The ability to control the quantum states of light is known as quantum light shaping. It is allowing researchers to target specific physical process in solid matter via photon absorption. Quantum light shaping can also be used to produce entanglement and generate single photons. Both capabilities are key components of quantum-logic operations, including quantum computing.

In 2012, the Steve Cundiff group developed a quantum light-shaping process that controls the quantum state distribution in ultrafast laser light without changing that light’s classical (normal) characteristics. The new technique is used in conjunction with conventional pulse-shaping techniques to create customized laser light. Quantum light shaping has made it possible to use quantum spectroscopy with any sample in the laboratory. As an added bonus, the new technique has the timing and accuracy of ordinary femtosecond spectroscopy.

The group recently investigated the quantum features of laser light by measuring the response of a semiconducting material as the light intensity of a laser was varied. Using this information and new theory developed by colleagues at Philipps-Universität Marburg, the researchers calculated what would have happened if they had manipulated the quantum nature of light in a superposition of two intensities. Such a superposition is called a “Schrödinger Cat,” or cat, state.

The technique works because the new theory made it possible to reconstruct the cat state by adding together two different intensities of normal laser light. The reconstruction is very handy because any attempt to measure the cat state would have resulted in the light being one intensity or the other, but not both simultaneously as in a cat state.

The group discovered that the response of their sample to light’s quantum behavior wasn’t straightforward. The response consisted of higher-frequency resonances (harmonics) that were only visible when the light was sufficiently intense. By listening for these harmonics and carefully measuring them, the group was able to reconstruct the sample’s response to light in a cat state.

This work demonstrated that light’s quantum features are important to an understanding of how a material responds to light. In the future, the group plans to apply its new quantum spectroscopy to different complex materials. The understanding gained from this research could lead to such customized optoelectronics devices as semiconductor lasers.

Semiconductor Nanostructures

The Steve Cundiff group studies the interaction of ultrashort laser pulses with semiconductors. In a semiconductor, electrons normally occupy the valence band. There, electrons cannot move freely because the band is full. However, the addition of energy to a semiconductor can excite electrons into the conduction band. In the conduction band, electrons move freely through a crystal or other semiconductor, allowing electrical currents to flow. One way to excite electrons is to shine the right color of light on them.

The group’s goal is to develop a deeper understanding of light-matter interactions. Such an understanding could lead to the design of better optoelectronic semiconductor-based devices. Cundiff and his colleagues are currently studying the quantum mechanical behavior of excitons in semiconductor quantum wells and quantum dots. Excitons are very large, fuzzy, and strongly interacting particles formed when a photo-excited electron in the conduction band binds with the positively charged hole it left behind in the valence band. Quantum wells confine charge-carrying particles called carriers in two dimensions, i.e., a thin layer. Quantum wells are thin enough that out-of-plane carrier motion is quantized. Quantum dots are semiconductors whose carriers (and therefore excitons) are confined in all three dimensions.

The Cundiff group studies coherence in direct-gap semiconductors such as GaAs with pump-probe spectroscopy, transient-four-wave mixing spectroscopy, and two-dimensional Fourier-transform spectroscopy (2DFTS) experiments. Most matter that has been resonantly excited by coherent laser light will remember the phase of the incident light for a period of time known as the dephasing time. For many types of matter, the dephasing time is tens of nanoseconds or longer. However, in a typical semiconductor, the dephasing time is usually less than a picosecond. The group has shown that this unusual response to optical excitation arises from carriers that are in extended states (i.e., their wave functions are spread over many lattice sites, not just a single atom). As a result, excitons interact strongly with each other, exhibiting interactive behavior not present in isolated atoms and molecules. This behavior is responsible for the dramatic difference in dephasing times between semiconductors and other materials.

The researchers have developed a technique that reveals previously hidden electronic interactions in semiconductors. By measuring the correlation between the phase of incident light and that of the emitted light, they have observed coupling among excitons. This technique provides a powerful probe into the underlying many-body physics of semiconductors.

Quantum mechanical behavior of semiconductor nanostructures

Electric fields alter the band structure of semiconductors, allowing new electronic transitions between the valence and conduction bands below the bandgap and causing oscillations above the bandgap. This change in the material’s absorption properties represents manifestations of complex quantum mechanical behavior. The Cundiff group conducts theoretical and experimental investigations aimed at better understanding the quantum mechanical behavior of semiconductor nanostructures.

For instance, the group recently was able to combine experiment and theory to create a “quantum spectroscopy.” The new method allowed to researchers to determine how a semiconductor nanostructure responded to light’s quantum features even though it was not possible to directly create light with those features. Instead, the researchers added together the effects of two different laser light intensities containing quantum superpositions of both intensities. The superpositions, called “cat” states, produced harmonics in the absorption of a semiconductor sample. Measurements of the harmonics allowed them to use a new theory to reconstruct the response of the sample to cat light. By averaging data taken over many days, the researchers were able to gain a more complete understanding how semiconductors respond to the quantum effects of light.

Quantum Droplets

The group recently shined a laser on a sample of gallium arsenide (GaAs) and created a fog of liquid-like quantum droplets, which they subsequently named dropletons. Dropletons are a new, stable form of matter much like an ordinary liquid, with one key difference. Dropletons contain charged particles, i.e., negatively charged electrons and positively charged "holes." Holes are like bubbles created when electrons in GaAs are excited by light.

Dropletons are structures containing multiple electrons and holes (for example 4,5, or 6 of each). Their structure is in between that of a traditional atom with a positively charged nucleus surrounded by negatively charged electrons and an older model of the atom that viewed it as a positively charged sphere with electrons embedded in it. They behave quantum mechanically because they contain only a few electrons and holes. The electrons and holes are not bound into pairs. All the electrons interact equally with all of the holes and vice versa.

According to the quantum-droplet theory calculations (as represented in the figure), the electron is in the middle of the tall structure in the middle of the droplet. The hole and the electron are most likely right on top of each other. However, the hole could also be just above, just below, or even next to the electron. The next most likely location of the hole is somewhere on the first ring. The third most likely location for the hole is on the second ring. The least likely location is in the gaps between the rings. As the density of electrons and holes increases inside a droplet, so too does the number of rings, as shown in the background of the figure.

Use of JILA MONSTR for semiconductor nanostructure studies

As part of its work on semiconductor nanostructures, the Cundiff group designed and built the JILA MONSTR (Multidimensional Optical Nonlinear SpecTRometer). The MONSTR is a compact, ultrastable optical platform containing nested and folded interferometers that can split an incoming coherent laser pulse into four identical pulses propagating parallel to one another on four corners of a square, as shown in the figure. The beams are focused into a sample and a coherent nonlinear optical signal is emitted and recorded by referencing it against one of the excitation pulses.

This 2DFTS system generates a signal that can be recorded in 1–3 time dimensions and Fourier-transformed into multidimensional frequency spectra. The MONSTR makes possible all-optical phase retrieval and provides a technique for finding the correct phase of emitted four-wave mixing signals. These capabilities allow the researchers to resolve the nonlinear polarization of interactions that reveal exciton resonances and other quantum phenomena.

The group has also investigated differences in how excitons interact depending on whether they’re stimulated by coherent laser light or laser light consisting of random phases of near-infrared wavelengths. The researchers wanted to better understand how this randomness (which researchers typically see as "noise") plays out in exciton interactions. They have also looked into modeling the electronic structure of semiconductor materials and studied the effects of applied electromagnetic fields on the spin-coherence properties of electrons in semiconductors. They’re also studying the effects of electric fields on the band structure of these materials.

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